This work seeks to develop, evaluate and use new MRI methods for non-invasive quantitative assessment of myocardial perfusion reserve (MPR). The methods will be designed to work robustly for patients with arrhythmias or poor ECG signals. The methods will be applied along with left ventricular (LV) and left atrial (LA) function and LA fibrosis measurements to study changes due to treatment for atrial fibrillation (AF). Specific aims are (1) To design and test highly-undersampled ungated perfusion acquisitions and reconstructions. (2) To provide robust quantitative perfusion estimates by improved processing and by identifying an accurate arterial input function using methods that are widely applicable across a range of doses and acquisition types. (3) To determine the validity and repeatability of the proposed quantitative methods and the differences in perfusion and MPR measured at systole and diastole, including determining if systole or diastole is most repeatable when quantifying perfusion. (4) To determine the changes over time in perfusion reserve and cardiac function and left atrial fibrosis, after ablative treatment for AF. This will allow for determining the extent of perfusion improvement acutely due to conversion to sinus rhythm and the degree of recovery of perfusion reserve that recovers more slowly over months. These aims will be accomplished by developing methods to acquire perfusion data continuously, without a gating signal. Gating will be accomplished by analyzing the data retrospectively. Advanced reconstruction methods that include low rank and spatiotemporal constraints, and that employ compensation for respiratory and cardiac motion, will be developed and tested with the rapidly acquired self-gated perfusion sequences. An accurate arterial input function will be obtained using constrained data- driven blind estimation techniques. The accuracy of the new methods will be determined by validation in an animal model of AF, and by comparison to human studies with dynamic PET, and the repeatability of the methods will be characterized. The serial application of the methods to patients undergoing ablation therapy will then provide new information regarding changes associated with myocardial remodeling. The development and use of such accurate and repeatable measurements of perfusion in humans will accelerate evaluation of clinical therapies, and provide new tools and knowledge for the management of patients with cardiac disease.